FReal direct

Overview

template <class Scalar, std::size_t N = 1>
struct FRealDirect : public RealDirect<FReal<Scalar, N>, FRealDirect<Scalar, N>>

The class FRealDirect has the same interface as FReal, but does not use expression templates for the operations: each operation returns an FRealDirect straight away. It is a drop-in replacement for FReal (see below), for existing code bases which may have issues integrating with expression templates; it also makes debugging easier.

Compatibility with FReal

FRealDirect is designed as a drop-in replacement for FReal in generic code, for example large numerical libraries that are templated on (or typedef) their floating point type. For first-order and higher-order direct mode types (such as FRealDirect<FRealDirect<double>>), XAD provides the same functionality as for FReal:

• Arithmetic and comparisons with the same type, with any built-in arithmetic type (including integer literals, e.g. x < 0 or 2 * x), with XAD expressions, and with types that implicitly convert to FRealDirect (for example a type with a conversion operator, like QuantLib's Null<Real>). As for FReal, higher-order types do not mix in arithmetic with their inner active type. Compound assignments and ++ / -- return a reference to FRealDirect.
• Conversions: implicit conversion from built-in arithmetic types, no implicit conversion to double or int (as for FReal), explicit conversion to bool and (with XAD_ALLOW_INT_CONVERSION, the default) explicit conversion to integer types via static_cast. FRealDirect is not constructible from unrelated types, so that std::is_constructible and std::is_convertible give the same answers as for FReal.
• Mathematical functions: all functions listed in Mathematical Operations, in the xad namespace and (after including XAD/StdCompatibility.hpp) in the std namespace, with the same mixed-argument overloads as FReal. All of them propagate derivatives.
• std compatibility (XAD/StdCompatibility.hpp): std::numeric_limits (all members, returning the underlying passive type as for FReal), std::hash, std::to_string, and the type traits std::is_floating_point, std::is_arithmetic, std::is_signed, std::is_fundamental, std::is_scalar, std::is_compound and std::is_trivially_copyable (including the C++17 _v variable templates).
• Complex numbers (XAD/Complex.hpp): std::complex<FRealDirect<T>> with the same operators and functions as std::complex<FReal<T>>.
• Stream operators << and >>.
• Mode interface: fwdd<T> and the higher-order mode classes use FRealDirect as the active type. Jacobian and Hessian helpers are available for FRealDirect<T> and FRealDirect<FRealDirect<T>>.